1. Field of the Invention
The present invention relates to an information processing method, an information processing apparatus, and a computer-readable recording medium recording an information processing program. More particularly, the present invention is suitably used for transforming one multidimensional information pattern into another multidimensional information pattern and for inversely transforming the multidimensional information pattern having been transformed.
2. Description of the Related Art
Heretofore, Fourier transform, Laplace transform, etc. have been known as information transforming methods for transforming one multidimensional information pattern into another multidimensional information pattern and for inversely transforming the multidimensional information pattern having been transformed.
On the other hand, a model utilizing a multidimensional discrete information pattern (M. Creutz, Computer in Physics 5, 198(1991)) has been proposed as a model capable of being inversely transformed.
Furthermore, a diffusion process described by a diffusion equation or the like is known as a method for transforming one multidimensional information pattern into another multidimensional information pattern.
However, the above conventional methods and model have problems as follows. Fourier transform, Laplace transform, etc. can be used with relatively easy analysis because of using numerical formula expressed in the simple form, but they are restricted in applications because of linear transform.
The model utilizing a multidimensional discrete information pattern cannot handle a continuous value, and therefore input information must be processed into the discrete form before starting transform of the information. Some of information is lost upon the processing into the discrete form.
The diffusion process described by a diffusion equation or the like is applicable only to forward transform, but not to inverse transform. Accordingly, the diffusion process has a difficulty in maintaining the amount of input information as it is.
It is therefore an object of the present invention is to provide an information processing method, an information processing apparatus, and a computer-readable recording medium recording an information processing program to implement the method and apparatus, which can transform one multidimensional information pattern into another multidimensional information pattern, is applicable to a wide range of applications, can handle a continuous value, and can prevent a loss of information.
Another object of the present invention is to provide an information processing method, an information processing apparatus, and a computer-readable recording medium recording an information processing program to implement the method and apparatus, which can transform one multidimensional information pattern into another multidimensional information pattern and inversely transform the multidimensional information pattern having been transformed, is applicable to a wide range of applications, can handle a continuous value, and can prevent a loss of information.
To achieve the above objects, a first aspect of the present invention provides an information processing method comprising an inputting step of inputting information carriers expressed by n-dimensional vectors (n is a natural number) to a number n of information carrier storing means which are distributed over an m-dimensional space (m is a natural number) and have the function of holding information carriers in a real number value; a processing step of repeating processing to apply a predetermined amount of information carriers to the information carrier storing means, to move a predetermined amount of information carriers among a predetermined set of the information carrier storing means, and to dissipate a predetermined amount of information carriers from the information carrier storing means; and an outputting step of outputting information carriers expressed by n-dimensional vectors from the number n of information carrier storing means.
A second aspect of the present invention provides an information processing method comprising an inputting step of inputting information carriers expressed by n-dimensional vectors (n is a natural number) to a number n of information carrier storing means which are distributed over an m-dimensional space (m is a natural number) and have the function of holding information carriers in a real number value; a processing step of repeating processing to apply a predetermined amount of information carriers to those of the information carrier storing means which are positioned in the vicinity of a geometrical surface, to move a predetermined amount of information carriers among a predetermined set of the information carrier storing means, and to dissipate a predetermined amount of information carriers from the information carrier storing means; and an outputting step of outputting information carriers expressed by n-dimensional vectors from the number n of information carrier storing means.
A third aspect of the present invention provides an information processing method comprising a first inputting step of inputting information carriers expressed by n-dimensional vectors (n is a natural number) to a number n of information carrier storing means which are distributed over an m-dimensional space (m is a natural number) and have the function of holding information carriers in a real number value; a first processing step of repeating processing to apply a predetermined amount of information carriers to the information carrier storing means, to move a predetermined amount of information carriers among a predetermined set of the information carrier storing means, and to dissipate a predetermined amount of information carriers from the information carrier storing means; a first outputting step of outputting information carriers expressed by n-dimensional vectors from the number n of information carrier storing means; a second inputting step of inputting the information carriers expressed by n-dimensional vectors and output in the first outputting step to the number n of information carrier storing means; a second processing step of repeating processing to apply a predetermined amount of information carriers to those of the information carrier storing means which are positioned in the vicinity of a geometrical surface, to move a predetermined amount of information carriers among a predetermined set of the information carrier storing means, and to dissipate a predetermined amount of information carriers from the information carrier storing means; and a second outputting step of outputting information carriers expressed by n-dimensional vectors from the number n of information carrier storing means.
A fourth aspect of the present invention provides an information processing apparatus employing a number n (n is a natural number) of information carrier storing means which are distributed over an m-dimensional space (m is a natural number) and have the function of holding information carriers in a real number value, the apparatus comprising an inputting function of inputting information carriers expressed by n-dimensional vectors to the information carrier storing means; a processing function of repeating processing to apply a predetermined amount of information carriers to the information carrier storing means, to move a predetermined amount of information carriers among a predetermined set of the information carrier storing means, and to dissipate a predetermined amount of information carriers from the information carrier storing means; and an outputting function of outputting information carriers expressed by n-dimensional vectors from the number n of information carrier storing means.
A fifth aspect of the present invention provides an information processing apparatus employing a number n (n is a natural number) of information carrier storing means which are distributed over an m-dimensional space (m is a natural number) and have the function of holding information carriers in a real number value, the apparatus comprising an inputting function of inputting information carriers expressed by n-dimensional vectors (n is a natural number) to the information carrier storing means; a processing function of repeating processing to apply a predetermined amount of information carriers to those of the information carrier storing means which are positioned in the vicinity of a geometrical surface, to move a predetermined amount of information carriers among a predetermined set of the information carrier storing means, and to dissipate a predetermined amount of information carriers from the information carrier storing means; and an outputting function of outputting information carriers expressed by n-dimensional vectors from the number n of information carrier storing means.
A sixth aspect of the present invention provides an information processing apparatus employing a number n (n is a natural number) of information carrier storing means which are distributed over an m-dimensional space (m is a natural number) and have the function of holding information carriers in a real number value, the apparatus comprising a first inputting function of inputting information carriers expressed by n-dimensional vectors (n is a natural number) to the information carrier storing means; a first processing function of repeating processing to apply a predetermined amount of information carriers to the information carrier storing means, to move a predetermined amount of information carriers among a predetermined set of the information carrier storing means, and to dissipate a predetermined amount of information carriers from the information carrier storing means; a first outputting function of outputting information carriers expressed by n-dimensional vectors from the number n of information carrier storing means; a second inputting function of inputting the information carriers expressed by n-dimensional vectors and output by the first outputting function to the information carrier storing means; a second processing function of repeating processing to apply a predetermined amount of information carriers to those of the information carrier storing means which are positioned in the vicinity of a geometrical surface, to move a predetermined amount of information carriers among a predetermined set of the information carrier storing means, and to dissipate a predetermined amount of information carriers from the information carrier storing means; and a second outputting function of outputting information carriers expressed by n-dimensional vectors from the number n of information carrier storing means.
A seventh aspect of the present invention provides an information processing apparatus comprising an input unit to which data expressed by n-dimensional vectors (n is a natural number) is input; a storage unit made up of a number n of information carrier storing means and storing the data input to the input unit; a control unit for repeatedly executing processing to apply a predetermined amount of information carriers to the data stored in the storage unit, to move a predetermined amount of information carriers, and to dissipate a predetermined amount of information carriers; a random number generating unit for generating a random number and sending the generated random number to the control unit; a determining unit for determining whether a change in amount of the information carriers in each of the information carrier storing means has become equal to or less than a predetermined value; and an output unit for outputting a processing result from the control unit.
An eighth aspect of the present invention provides a recording medium recording an information processing program and being readable by a computer, the program comprising an inputting step of inputting information carriers expressed by n-dimensional vectors (n is a natural number) to a number n of information carrier storing means which are distributed over an m-dimensional space (m is a natural number) and have the function of holding information carriers in a real number value; a processing step of repeating processing to apply a predetermined amount of information carriers to the information carrier storing means, to move a predetermined amount of information carriers among a predetermined set of the information carrier storing means, and to dissipate a predetermined amount of information carriers from the information carrier storing means; and an outputting step of outputting information carriers expressed by n-dimensional vectors from the number n of information carrier storing means.
A ninth aspect of the present invention provides a recording medium recording an information processing program and being readable by a computer, the program comprising an inputting step of inputting information carriers expressed by n-dimensional vectors (n is a natural number) to a number n of information carrier storing means which are distributed over an m-dimensional space (m is a natural number) and have the function of holding information carriers in a real number value; a processing step of repeating processing to apply a predetermined amount of information carriers to those of the information carrier storing means which are positioned in the vicinity of a geometrical surface, to move a predetermined amount of information carriers among a predetermined set of the information carrier storing means, and to dissipate a predetermined amount of information carriers from the information carrier storing means; and an outputting step of outputting information carriers expressed by n-dimensional vectors from the number n of information carrier storing means.
A tenth aspect of the present invention provides a recording medium recording an information processing program and being readable by a computer, the program comprising a first inputting step of inputting information carriers expressed by n-dimensional vectors (n is a natural number) to a number n of information carrier storing means which are distributed over an m-dimensional space (m is a natural number) and have the function of holding information carriers in a real number value; a first processing step of repeating processing to apply a predetermined amount of information carriers to the information carrier storing means, to move a predetermined amount of information carriers among a predetermined set of the information carrier storing means, and to dissipate a predetermined amount of information carriers from the information carrier storing means; a first outputting step of outputting information carriers expressed by n-dimensional vectors from the number n of information carrier storing means; a second inputting step of inputting the information carriers expressed by n-dimensional vectors and output in the first outputting step to the number n of information carrier storing means; a second processing step of repeating processing to apply a predetermined amount of information carriers to those of the information carrier storing means which are positioned in the vicinity of a geometrical surface, to move a predetermined amount of information carriers among a predetermined set of the information carrier storing means, and to dissipate a predetermined amount of information carriers from the information carrier storing means; and a second outputting step of outputting information carriers expressed by n-dimensional vectors from the number n of information carrier storing means.
In the present invention, information carriers may be in any of the discrete and continuous form. Also, there are basically no restrictions on geometrical distribution of the number n of information carrier storing means over the m-dimensional space. For example, the information carrier storing means may be distributed in either regular or irregular array. Further, m and n may be each basically any natural number, but m is typically equal to or less than 3.
The processing step or function in the first, fourth and eighth aspect of the present invention, and the first processing step or function in the third, sixth and tenth aspect of the present invention each typically include a step or function of applying a predetermined amount of information carriers to the number n of information carrier storing means at random.
The processing step or function in the first, second, fourth, fifth, eighth and ninth aspect of the present invention, and the first processing step or function and the second processing step or function in the third, sixth and tenth aspect of the present invention each typically includes a diffusing step or function of moving the information carriers in each of the information carrier storing means to the information carrier storing means which are positioned in the vicinity of each information carrier storing means. The diffusing step is typically a step of diffusing the information carriers in the number n of information carrier storing means through nonlinear diffusion to the information carrier storing means which are positioned in the vicinity of each of the information carrier storing means.
The nonlinear diffusion is expressed, for example, by the following formula (1);
z(r,t+h)=z(r,t)+hxc2x7(R(r,t)+Dxc2x7∇2f(z(r,t))xe2x88x92d(r,t))xe2x80x83xe2x80x83(1)
where r is spacial coordinate of each of the information carrier storing means, t is time, z(r,t) is an amount of information carriers stored in the information carrier storing means corresponding to the spacial coordinate r and the time t, h is a differential parameter, R(r,t) is a function representing the amount of applied information carriers, D is a diffusion constant, f(z(r,t)) is a function defined by the following formula (2), and d(r,t) is a function representing the dissipation of information carriers, and the following formula (2);                               f          ⁡                      (                          z              ⁡                              (                                  r                  ,                  t                                )                                      )                          =                  1                      1            +                          exp              ⁡                              [                                  -                                      β                    ⁡                                          (                                                                        z                          ⁡                                                      (                                                          r                              ,                              t                                                        )                                                                          -                                                  z                          0                                                                    )                                                                      ]                                                                        (        2        )            
where xcex2 and z0 are each a predetermined constant. In the above formulae, xcex2 is usually set such that a maximum value of natural numbers resulting from the n-dimensional vectors output in the outputting step or function, or the first outputting step or function, or the second outputting step or function is equal to the value obtained by subtracting one from the number of the information carrier storing means which are positioned in the vicinity of each of the information carrier storing means.
The processing step or function in the first, second, fourth, fifth, eighth and ninth aspect of the present invention, and the first processing step or function and the second processing step or function in the third, sixth and tenth aspect of the present invention each typically includes a step of dissipating the information carriers from the information carrier storing means which are positioned in the vicinity of a surface defined by a distributed group of the number n of information carrier storing means.
The processing step or function in the first, second, fourth, fifth, eighth and ninth aspect of the present invention, and the first processing step or function and the second processing step or function in the third, sixth and tenth aspect of the present invention each typically further includes a step of dissipating the information carriers from the number n of information carrier storing means.
The processing step or function in the second, fifth and ninth aspect of the present invention, and the second processing step or function in the third, sixth and tenth aspect of the present invention each typically includes
The processing step or function in the first, second, fourth, fifth, eighth and ninth aspect of the present invention, and the first processing step or function and the second processing step or function in the third, sixth and tenth aspect of the present invention each typically includes a step of applying a predetermined amount of information carriers to the information carrier storing means which are positioned in the vicinity of a surface defined by a distributed group of the number n of information carrier storing means.
The processing step or function in the first, fourth and eighth aspect of the present invention, and the first processing step or function in the third, sixth and tenth aspect of the present invention each typically applies information carriers in such an amount that an integral value becomes equal to the product of the number of the information carrier storing means, which are positioned in the vicinity of each of the information carrier storing means, and n.
The processing step or function in the first, fourth and eighth aspect of the present invention, and the first processing step or function in the third, sixth and tenth aspect of the present invention each typically includes a step of binary-coding each element of the information carriers expressed by n-dimensional vectors.
With the present invention thus constructed, one multidimensional information pattern can be transformed into another multidimensional information pattern by inputting information carriers expressed by n-dimensional vectors, i.e., a multidimensional information pattern in general, to a number n of information carrier storing means which are distributed over an m-dimensional space; repeating processing to apply information carriers to the information carrier storing means, to move information carriers among a predetermined set of the information carrier storing means, and to dissipate information carriers from the information carrier storing means; and outputting a processing result in the form of information carriers expressed by n-dimensional vectors. Then, the multidimensional information pattern having been transformed can be inversely transformed by inputting the multidimensional information pattern having been transformed, i.e., the information carriers expressed by n-dimensional vectors, to the number n of information carrier storing means; repeating processing to apply information carriers to those of the information carrier storing means which are positioned in the vicinity of a geometrical surface, to move information carriers among a predetermined set of the information carrier storing means, and to dissipate information carriers from the information carrier storing means; and outputting a processing result in the form of information carriers expressed by n-dimensional vectors. Since both the forward transform and the inverse transform can be performed, novel information processing between an input space and another space can be achieved in a similar way to Fourier transform, Laplace transform, etc. which have been often employed so far. In particular, since the information carriers are moved through nonlinear diffusion expressed by the formulae (1) and (2), it becomes possible to achieve engineering applications to processing that has been difficult to achieve with the conventional linear transform. Further, since both the types of transform according to the present invention can deal with continuous values, there is no need of processing input information into the discrete form before starting transform of the information, and therefore a loss of information can be prevented.